| Ch. 1 | Introduction | 1 |
| Ch. 2 | Jordan Algebras and the Mixed Linear Model | 5 |
| 2.2 | Square Matrices and Jordan Algebras | |
| 2.3 | Idempotents and Identity Elements | |
| 2.4 | Equivalent Definitions for a Jordan Algebra | |
| 2.5 | Jordan Algebras Derived from Real Symmetric Matrices | |
| 2.6 | The Algebraic Study of Random Quadratic Forms | |
| 2.7 | The Statistical Study of Random Quadratic Forms | |
| 2.8 | Covariance Matrices Restricted to a Convex Space | |
| 2.9 | Applications to the General Linear Mixed Model | |
| Ch. 3 | Further Technical Results on Jordan Algebras | 42 |
| 3.1 | The JNW Theorem | |
| 3.2 | The Classes of Simple, Formally Real, Special Jordan Algebras | |
| 3.3 | The Jordan and Associative Closures of Subsets of S[subscript m] | |
| 3.4 | Subspaces of [actual symbol not reproducible] | |
| 3.5 | Solutions of the Equation: sasbs = 0 | |
| Ch. 4 | Jordan Algebras and the EM Algorithm | 63 |
| 4.2 | The General Patterned Covariance Estimation Problem | |
| 4.3 | Precise State of the Problem | |
| 4.4 | The Key Idea of Rubin and Szatrowski | |
| 4.5 | Outline of the Proposed Method | |
| 4.6 | Preliminary Results | |
| 4.7 | Further Details of the Proposed Method | |
| 4.8 | Estimation in the Presence of Missing Data | |
| 4.9 | Some Conclusions about the General Solution | |
| 4.10 | Special Cases of the Covariance Matrix Estimation Problem: Zero Constraints | |
| 4.11 | Embeddings for Constant Diagonal Symmetric Matrices | |
| 4.12 | Proof of the Embedding Problem for Sym(m)[subscript c] | |
| 4.13 | The Question of Nuisance Parameters | |
| Index | 96 |
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